A new look at the moduli space of stable hyperelliptic curves

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We carry out the log minimal model program for the moduli space (H) over bar (g) of stable hyperelliptic curves and show that certain log canonical models of (H) over bar (g) are isomorphic to the proper transform of (H) over bar (g) in the corresponding log canonical models of (M) over bar (g). For g = 3, we retrieve the compact moduli space (B) over bar (8) of binary forms as a log canonical model, and obtain a decomposition of the natural map (H) over bar (3) -> (B) over bar (8) into successive divisorial contractions of the boundary divisors. As a byproduct, we also obtain an isomorphism of (B) over bar (8) with the GIT quotient of the Chow variety of bicanonically embedded hyperelliptic curves of genus three.
Publisher
SPRINGER
Issue Date
2010-02
Language
English
Article Type
Article
Citation

MATHEMATISCHE ZEITSCHRIFT, v.264, no.2, pp.317 - 326

ISSN
0025-5874
DOI
10.1007/s00209-008-0466-7
URI
http://hdl.handle.net/10203/104145
Appears in Collection
MA-Journal Papers(저널논문)
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